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<span class="kw">let </span><font color="Maroon" title="c1">cc</font>, <font color="Maroon" title="c2">aa</font>, <font color="Maroon" title="c3">bb</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>   st <font color="Maroon" title="c1">cc</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span> &amp; <font color="Maroon" title="c1">cc</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span> holds <br/> <a href="sfmastr3.html#K4" title="SFMASTR3:func.4">swap</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c1">cc</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">cc</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span> &amp; <font color="Maroon" title="c1">cc</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span> implies  <a href="sfmastr3.html#K4" title="SFMASTR3:func.4">swap</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c1">cc</font> )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">a</font> = <font color="Maroon" title="c2">aa</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">b</font> = <font color="Maroon" title="c3">bb</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">aux1</font> = 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">aux2</font> = 2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span>;<br/>
<span class="kw">assume </span><a NAME="E1:48"/>
( <font color="Maroon" title="c1">cc</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span> &amp; <font color="Maroon" title="c1">cc</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p1"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="sfmastr3.html#K4" title="SFMASTR3:func.4">swap</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c1">cc</font></span><br/>

<a NAME="E2:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A1</font></span>: 
( <span class="p1">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p2"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">does_not_destroy</a> <font color="Maroon" title="c1">cc</font> &amp; <span class="p1">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p2"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">bb</font> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">does_not_destroy</a> <font color="Maroon" title="c1">cc</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#T20" title="SCMFSA7B:th.20">SCMFSA7B:20</a></span>;<br/>
<a NAME="E3:48"/>
<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p1">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p2"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa7b.html#R3" title="SCMFSA7B:pred.3">does_not_destroy</a> <font color="Maroon" title="c1">cc</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#T21" title="SCMFSA7B:th.21">SCMFSA7B:21</a></span>;<br/>
<a NAME="E4:48"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="sfmastr1.html#NK7" title="SFMASTR1:NK.7">-stRWNotIn</a> <span class="p4"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font></span>)</span> <a href="scmfsa6a.html#K8" title="SCMFSA6A:func.8">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p4"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">bb</font></span>)</span></span>)</span> <a href="scmfsa6a.html#K7" title="SCMFSA6A:func.7">';'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p2">(<span class="default">2 <a href="sfmastr1.html#NK8" title="SFMASTR1:NK.8">-ndRWNotIn</a> <span class="p3"><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">{</a><span class="default"><font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font></span><a href="sfmastr1.html#K2" title="SFMASTR1:func.2">}</a></span></span>)</span></span>)</span> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c1">cc</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:48"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="scmfsa8c.html#T83" title="SCMFSA8C:th.83">SCMFSA8C:83</a>, <a class="ref" href="scmfsa8c.html#T84" title="SCMFSA8C:th.84">SCMFSA8C:84</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:48"/>
 <a href="sfmastr3.html#K4" title="SFMASTR3:func.4">swap</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">aa</font>,<font color="Maroon" title="c3">bb</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">does_not_destroy</a> <font color="Maroon" title="c1">cc</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#T21" title="SCMFSA7B:th.21">SCMFSA7B:21</a>, <a class="ref" href="scmfsa8c.html#T83" title="SCMFSA8C:th.83">SCMFSA8C:83</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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